since i'm perhaps a bit more well rounded in headphones i thought i would jump in. keep in mind that its hard to be familiar with all headphones so there are many more obscure choices (which may be just as great) which are not recommended here but i've highlighted many of the common ones.
what type of headphone is best for you depends on what you expect in terms of sound signature:
headphones like the audiotechncia ad500x/700x/900x, akg k701 and grados are tuned for treble and mids and will all have near zero low bass response but fair mid bass response. the ad series is known for its huge soundstage and great positional audio. the akg and grados will be more shrill/bright over the ad series. this type of headphone is good if you want to game with an advantage (hear footsteps easier in fps) or if you dont like bass. these are all open cans.
cans like the audiotechnica m50x, beyerdynamic dt770, sennheiser hd280/380 or v-moda are all more bassy cans with reduced soundstage, v-shaped sound signature (more treble and bass than mids) and more bass than neutral. while not as ideal for gaming, they are nice for users looking for something which muffles outside noises and is on the bassy side of things. the m50x (i own a m50 myself) is fairly poor in soundstaging and positional audio (but otherwise has good sound). the dt770 is much better in all regards. these are all closed cans.
the sennheiser dt990 is both an open can for the large soundstaging and great positional audio combined with a v-shaped sound profile for a more exciting sound. despite being open cans which normally lack bass they are also suprisingly bassy but still have nice crisp bright highs (some might want to tone the highs down a bit). basically sort of a best of both worlds. the dt880 is a more neutral version of this more akin to the section below - but less mellow.
the sennheiser hd518/558/598 are more neutral with a fairly flat sound. the 598 is closest to neutral with the biggest soundstage with the 518 the closest to peaking a bit on bass and the least soundstage but not by a huge degree as all of them use the exact same drivers and the differences are due to design only. they are also fairly easy listening and are more mellow and not as bright as some choices.
amps - generally not needed unless you specifically have a pair of headphones which is hard to drive (the beyer dt series) or if you're looking to tone down the brightness of a headphone with a more warm amplifier (such as dt990, akg cans, grados). otherwise, a good soundcard is likely a better option overall. depending on what you wanted to get... something like the xonar dx, creative z or xonar dg would work. if you did need an amplifier, fiio makes some good budget amps which would work and add a more warm sound signature to warm up cool or tone down bright headphones just a tad.
as for microphones, the best boom-style microphone for attaching to headphones is the modmic bought from their website. i believe they ship worldwide. an alternative is the not-as-nice moovemic, getting a stereo lavalier mic and using an adapter or going with a nice desktop mic - preferably with boom arm.
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to suggest a headphone for you what do we need?
-prices. let us know how much you would pay for the various models discussed.
-preferences. let us know which sounds the most appealing to you - if you can listen to them in person that would be MOST ideal but not always possible
-equipment. if you need to purchase a soundcard, amps, etc. we would need to factor this in. see what things like the soundcards discussed or amps discussed would cost you
-comfort. let us know if you have large ears, a big head, glasses or other things which could influence comfort.
-other. let us know if you need them to block out noise, need more than standard bass, want virtual surround sound or other such needs.
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what has been discussed so far:
the hd598 and hd558 are both good, common choices and you usually cant go wrong.
akg and grado cans are more of a like it or hate it scenario.
the m50x while being good sounding is not ideal for gaming. if you wanted one, get the dt770 instead.
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clarification:
an amplifier does NOT remove electrical noise from an analog signal coming from your pc. an amplifier only increases the power level of the signal. if noise is present it will be still in the output.
a DAC (digital analog converter) however (and some amplifiers are paired up with a DAC in one box) will normally remove any said electrical noise as they are external to the system.
the negative to using an external DAC is that you lose out on virtual surround processing that many soundcards may give you. the benefit is that you get reduced noise (though soundcards also do this so its not really a win).
keep in mind that you might still be affected by usb noise or ground loop (dont worry about this, i'm just noting it for completeness and it doesnt normally happen to most people) even if you were connected via usb with an external DAC. this however is more of an isolated case-by-case basis scenario and there are ways to eliminate it.
which is superior? neither. both have their own benefits.
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if you absolutely needed a headset and did not want a headphone and separate mic solution what is out there which actually sounds good?
the sennheiser g4me zero, g4me one, pc363d. the beyerdynamic mmx300. the audiotechncia ath-adg1. all are based on headphone designs by the respective companies. all are also overpriced completely when you consider the price of buying the headphone they are based on and adding a mic (and sometimes a soundcard) to them which makes them not as nice price/performance wise but no less good sounding. most of them are fairly light on bass however (notably the mmx300 and adg1.. the senn's are not bass-heavy but not quite as weak).